Text: # Load in your data set concrete <- read.csv(file = "concrete.csv", header = T)
# Set seed: use the last four digits of your student ID set.seed(....)
# Take a random sample of 200 observations concrete_sample <- concrete[sample(nrow(concrete), 200, )]
You will now have a random sample of 200 observations from the cement data set, unique to you, stored in a new data frame called cement_sample.
Questions
Once you have completed the steps above, use R to answer the following questions. Remember to include all your R code and output in your submission.
Note: You must carry out your analysis on this sample of 200. You will lose marks if you analyze any other data set, including the entire concrete.csv data set.
(a) Using Question 5 of the Week 10 Computer Lab as a guide, use the lm function to estimate a Multiple Linear Regression model for compressive_strength (Y) on cement (X1), fly-ash (X2), superplasticizer (X3), and fine_aggregate (X4), saving your estimated model as an object with a name of your choice. Next, use the summary function to display the least squares estimates and other associated output for your model. Provide the code you used to answer this question (including the commands used to generate your random sample) as well as a copy of your results. (3 marks)
(b) Create a residuals versus fitted values plot and a normal Q-Q plot of the standardized residuals (2 marks)
(c) Do you think that either of the plots you have created in part (b) suggest that there are any linear regression model violations with which we need to be concerned? Justify your answer with reference to both of the plots. (3 marks)
(d) Regardless of your answer to (c), for the remainder of this question please assume that there are no linear regression model violations. Write out the estimated equation for your regression model, based on the R output provided by the summary function. (2 marks)
(e) Does your regression model fit the data well? Explain (2 marks)
